det.cpp

强大的C++库

/*!
 * \file
 * \brief Implementation of determinant calculations
 * \author Tony Ottosson
 *
 * -------------------------------------------------------------------------
 *
 * IT++ - C++ library of mathematical, signal processing, speech processing,
 *        and communications classes and functions
 *
 * Copyright (C) 1995-2008  (see AUTHORS file for a list of contributors)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * -------------------------------------------------------------------------
 */

#include <itpp/base/algebra/det.h>
#include <itpp/base/algebra/lu.h>


namespace itpp {


  /* Determinant of square matrix.
     Calculate determinant of inmatrix (Uses LU-factorisation)
     (See Theorem 3.2.1 p. 97 in Golub & van Loan, "Matrix Computations").

     det(X) = det(P')*det(L)*det(U) = det(P')*1*prod(diag(U))
  */
  double det(const mat &X)
  {
    it_assert_debug(X.rows()==X.cols(),"det : Only square matrices");

    mat L, U;
    ivec p;
    double s=1.0;
    int i;

    lu(X,L,U,p); // calculate LU-factorisation

    double temp=U(0,0);
    for (i=1;i<X.rows();i++) {
      temp*=U(i,i);
    }

    // Calculate det(P'). Equal to (-1)^(no row changes)
    for (i=0; i<p.size(); i++)
      if (i != p(i))
	s *=-1.0;

    return temp*s;
  }


  /* Determinant of complex square matrix.
     Calculate determinant of inmatrix (Uses LU-factorisation)
     (See Theorem 3.2.1 p. 97 in Golub & van Loan, "Matrix Computations").

     det(X) = det(P')*det(L)*det(U) = det(P')*1*prod(diag(U))

     Needs LU-factorization of complex matrices (LAPACK)
  */
  std::complex<double> det(const cmat &X)
  {
    it_assert_debug(X.rows()==X.cols(),"det : Only square matrices");

    int i;
    cmat L, U;
    ivec p;
    double s=1.0;

    lu(X,L,U,p); // calculate LU-factorisation

    std::complex<double> temp=U(0,0);
    for (i=1;i<X.rows();i++) {
      temp*=U(i,i);
    }

    // Calculate det(P'). Equal to (-1)^(no row changes)
    for (i=0; i<p.size(); i++)
      if (i != p(i))
	s *=-1.0;

    return temp*s;
  }


} // namespace itpp